Katz centrality

About: Katz centrality is a research topic. Over the lifetime, 601 publications have been published within this topic receiving 77858 citations.

Optimal Multiphase Investment Strategies for Influencing Opinions in a Social Network

Abstract: We study the problem of optimally investing in nodes of a social network in a competitive setting, where two camps aim to maximize adoption of their opinions by the population. In particular, we consider the possibility of campaigning in multiple phases, where the final opinion of a node in a phase acts as its initial biased opinion for the following phase. Using an extension of the popular DeGroot-Friedkin model, we formulate the utility functions of the camps, and show that they involve what can be interpreted as multiphase Katz centrality. Focusing on two phases, we analytically derive Nash equilibrium investment strategies, and the extent of loss that a camp would incur if it acted myopically. Our simulation study affirms that nodes attributing higher weightage to initial biases necessitate higher investment in the first phase, so as to influence these biases for the terminal phase. We then study the setting in which a camp's influence on a node depends on its initial bias. For single camp, we present a polynomial time algorithm for determining an optimal way to split the budget between the two phases. For competing camps, we show the existence of Nash equilibria under reasonable assumptions, and that they can be computed in polynomial time.

Centrality analysis for modified lattices

Abstract: We derive new, exact expressions for network centrality vectors associated with classical Watts-Strogatz style "ring plus shortcut" networks. We also derive easy-to-interpret approximations that are highly accurate in the large network limit. The analysis helps us to understand the role of the Katz parameter and the PageRank parameter, to compare linear system and eigenvalue based centrality measures, and to predict the behavior of centrality measures on more complicated networks.

Interplay between Social Influence and Network Centrality: Shapley Values and Scalable Algorithms

Abstract: A basic concept in network analysis is centrality, which measures the importance of nodes in a network. In this research, we address the following fundamental question: "Given a social network, what is the impact of the social influence models on network centrality?" Social influence is commonly formulated as a stochastic process, which defines how each group of nodes can collectively influence other nodes in an underlying graph. This process defines a natural cooperative game, in which each group's utility is its influence spread. Thus, fundamental game-theoretical concepts of this social-influence game can be instrumental in understanding network influence. We present a comprehensive analysis of the effectiveness of the game-theoretical approach to capture the impact of influence models on centrality. In this paper, we focus on the Shapley value of the above social-influence game. Algorithmically, we give a scalable algorithm for approximating the Shapley values of a large family of social-influence instances. Mathematically, we present an axiomatic characterization which captures the essence of using the Shapley value as the centrality measure to incorporate the impact of social-influence processes. We establish the soundness and completeness of our representation theorem by proving that the Shapley value of this social-influence game is the unique solution to a set of natural axioms for desirable centrality measures to characterize this interplay. The dual axiomatic-and-algorithmic characterization provides a comparative framework for evaluating different centrality formulations of influence models. Empirically, through a number of real-world social networks --- both small and large --- we demonstrate the important features of the Shapley centrality as well as the efficiency of our scalable algorithm.

The Parameterized Complexity of Centrality Improvement in Networks

Abstract: The centrality of a vertex v in a network intuitively captures how important v is for communication in the network. The task of improving the centrality of a vertex has many applications, as a higher centrality often implies a larger impact on the network or less transportation or administration cost. In this work we study the parameterized complexity of the NP-complete problems Closeness Improvement and Betweenness Improvement in which we ask to improve a given vertex’ closeness or betweenness centrality by a given amount through adding a given number of edges to the network. Herein, the closeness of a vertex v sums the multiplicative inverses of distances of other vertices to v and the betweenness sums for each pair of vertices the fraction of shortest paths going through v. Unfortunately, for the natural parameter “number of edges to add” we obtain hardness results, even in rather restricted cases. On the positive side, we also give an island of tractability for the parameter measuring the vertex deletion distance to cluster graphs.

Modularity matrix of networks and the measure of community structure

Abstract: The relationships between positive （negative） eigenspectrums and the structure properties of community （anti-community） of complex networks are investigated, and some corresponding definitions are given. By using the multieigenspectrums of modularity matrix of networks, a kind of structural centrality measure called the community centrality, is introduced. This individual centrality measure describes the strength that the individual adheres to the corresponding community. The measure is illustrated and compared with the standard centrality measures using several artificial networks and real world networks data. The results show that the community centrality has better discrimination, and it has positive correlation with the degree centrality.